Andy Ellam submitted a 1991 cite from a quote by Frederik Pohl on the back of an edition of Larry Niven's "Ringworld".
Matt Freestone submitted a cite from John Clute's 1988 book "Strokes"; Mike Christie verified the cite in the original 1982 magazine publication.
Lucius Sorrento submitted a cite from a 1996 book quoting a review by P. Schuyler Miller; Mike Christie verified it in the original 1957 magazine appearance.
Jeff Prucher submitted a 1997 cite from SF Studies.
Jeff Prucher submitted a 1989 cite from Norman Spinrad's book review column in Asimov's.
Mike Christie submitted a 2003 cite from John Cramer's column "The New Recycling Universe" in Analog.
Malcolm Farmer submitted a 1974 cite from a reprint of "William Atheling's" (James Blish's) 1970 "More Issues at Hand".

We are looking for cites for both "hard SF" and "hard science fiction".

Citations for hard science fiction n.

It is also very characteristic of the best ‘hard’ science fiction of its day.

1970‘W. Atheling’More Issues at Hand 99

Wells used the term originally to cover what we would today call ‘hard’ science fiction, in which a conscientious attempt to be faithful to already known facts (as of the date of writing) was the substrate on which the story was to be built, and if the story was also to contain a miracle, it ought at least not to contain a whole arsenal of them.

1982D. HartwellThe Golden Age of Science Fiction is Twelve in Top of News (1982, issue number unknown) 14

This is a quick rundown of the main possibilities an omnivore might fix on: classic fantasy (ghost stories, legends, tales); supernatural horror (two categories: classic—from Le Fanu, Blackwood, and Machen to Stephen King and Rosemary's Baby ; and Lovecraftian, the school of H. P. Lovecraft and his followers); Tolkienesque fantasy (in the manner of Lord of the Rings—carefully constructed fantasy worlds as the setting for a heroic quest); heroic fantasy (barely repressed sex fantasy in which a muscular, sword-bearing male beats monsters, magicians, racial inferiors, and effete snobs by brute force, then services every willing woman in sight—and they are all willing); Burroughsian science fantasy (adventure on another planet or thinly rationalized SF setting in which fantasy and anachronism—sword fighting among the stars—are essentials); space opera (the Western in space); hard science fiction (the SF idea is the center of attention, usually involving chemistry or physics or astronomy); soft science fiction (two alternate types: one in which the character is more important than the SF idea; the other focusing on any science other than physics or chemistry).

By hard science fiction we mean that science fiction in which the story turns around a change in the environment that can be understood only scientifically and generally through what are known as the hard sciences, usually the laboratory sciences such as chemistry, physics, and biology, and the observational sciences such as astronomy, geology, and geography. Mathematics and computers are two of the tools used by all the hard sciences. These sciences are considered hard because they deal with objective data, and predictions can be made from these data that are verifiable.

1988S. McCrumbBimbos of Death Sun v. 52

It's a good book. For hard science fiction, that is. It's scientifically sound.

1989Isaac Asimov's Sci. Fiction Mag. Dec. 186/1

Gregory Benford might take some issue with this notion‥with his metaphor of all science fiction which is not hard science fiction being like ‘playing tennis with the net down’, meaning that hard science fiction is that science fiction which eschews violation of the presently known laws of the continuum.

1990C. Sheffield in Thrust Winter 18/3

Someone, to help me pass the time, handed me a copy of‥Ringworld‥. I read it, and I said to myself, ‘Hey, hard science fiction is not dead.’

1991F. Pohl(back cover quote) in L. Niven Ringworld (back cover)

‘Ringworld’ is the best of the newest wave, the return to classical hard-science fiction of the kind popular in the Golden Age. Niven's imagination is 3-D and detailed, and his style is lucid and appealing.

1993Science-Fiction Studies July 158

Miller's first use of the exact term ‘“hard” science fiction’ came as early as November 1957, when he said that John W. Campbell, Jr.'s Islands of Space‘is also very characteristic of the best “hard” science fiction of its day’ (143). In February, 1960, he said that George O. Smith ‘has written some of the best “hard” science fiction we have—such as his “Venus Equilateral”’ (166). Two years later, he called A Fall of Moondust‘“hard” science fiction—the kind that many scientists and engineers are thinking of when they complain that the current brand is no good, or isn't even science fiction’

1993Science-Fiction Studies July 158

The term kept coming up in the 1960s and 1970s; he said that Clifford D. Simak's ‘Limiting Factor’‘is a puzzle story‥.perhaps the closest to “hard” science fiction in “the anthology under review”’ (9/62 155)‥.In December, 1963, he referred to ‘“hard” science fiction—the technical kind’ (86); in May, 1964, he said Fred and Geoffrey Hoyle's Fifth Planet was ‘to a degree a “hard”-type story which might even stir some interest in Hal Clement, chief sculptor of that form’ (87); in the same issue he commented, ‘Maybe we're short of the “hard” technical science fiction of the early years’ (89).

1994SFRA Rev. July 35

This trilogy makes use of many hard science fiction themes.

1994B. BovaCraft of Writing Sci. Fict. that Sells ii. 9

Every time I hear the term ‘hard science fiction’, I think to myself, ‘Hard?’ It's goddamned exhausting, that's what it is!’

1994Interzone Oct. 64/1

Its motifs have been plundered by these neighbouring genres to the extent that purists have been forced to designate a special category of ”hard science fiction“ to distinguish the sf which aims for some kind of extrapolative rigour from that which simply uses the imagery of sf as window-dressing.

1994Interzone Sept. 59/1

There was a time when genre fantasy was a mere annexe of the science-fiction marketplace. Nowadays, fantasy has the marketplace clout and the classic motifs of science fiction are increasingly being relegated to the status of stock ideas which can be deployed without discrimination alongside the traditional motifs of fantasy. It has been necessary to invent a special category of sf (“hard science fiction”) to distinguish that fugitive enclave of the marketplace where some sense of intellectual responsibility supposedly still holds, while more or less anything goes outside its beleaguered walls.